标题： 近超流体-莫特绝缘体相变处的玻色气体两体接触 显示英文标题

标题： Two-body contact of a Bose gas near the superfluid--Mott-insulator transition

摘要： 两体接触是稀薄玻色气体的基本量，它将热力学与短距离两体关联联系起来。 对于光学晶格中的玻色气体，在超流-莫特绝缘体相变附近，可以从压力的奇异部分$P-P_{\rm MI}$定义一个“普适”接触$C_{\rm univ}$（$P_{\rm MI}$是莫特绝缘体的压力）。 其表达式$C_{\rm univ}=C_{\rm DBG}(|n-n_{\rm MI}|,a^*)$在考虑量子临界点（QCP）处准粒子的有效“散射长度”$a^*$而不是真空中的散射长度时，与稀薄玻色气体的表达式一致，并且考虑了相对于莫特绝缘体的粒子（或空穴）的过量密度$|n-n_{\rm MI}|$。 在相变附近足够接近时，布里渊区中存在一个宽广的动量范围，其中动量分布的奇异性$n^{\rm sing}_{\bf k}=n_{\bf k}-n^{\rm MI}_{\bf k}$展现出高动量尾部$Z_{\rm QP} C_{\rm univ}/|{\bf k}|^4$，其中$Z_{\rm QP}$为量子涨落在QCP处的基本激发的准粒子权重。我们认为，接触$C_{\rm univ}$可以在当前最先进的光学晶格中的玻色气体实验以及磁绝缘体实验中测量。 显示英文摘要

摘要： The two-body contact is a fundamental quantity of a dilute Bose gas which relates the thermodynamics to the short-distance two-body correlations. For a Bose gas in an optical lattice, near the superfluid--Mott-insulator transition, a ``universal'' contact $C_{\rm univ}$ can be defined from the singular part $P-P_{\rm MI}$ of the pressure ($P_{\rm MI}$ is the pressure of the Mott insulator). Its expression $C_{\rm univ}=C_{\rm DBG}(|n-n_{\rm MI}|,a^*)$ coincides with that of a dilute Bose gas provided we consider the effective ``scattering length'' $a^*$ of the quasi-particles at the quantum critical point (QCP) rather than the scattering length in vacuum, and the excess density $|n-n_{\rm MI}|$ of particles (or holes) with respect to the Mott insulator. Sufficiently close to the transition, there is a broad momentum range in the Brillouin zone where the singular part $n^{\rm sing}_{\bf k}=n_{\bf k}-n^{\rm MI}_{\bf k}$ of the momentum distribution exhibits the high-momentum tail $Z_{\rm QP} C_{\rm univ}/|{\bf k}|^4$, where $Z_{\rm QP}$ the quasi-particle weight of the elementary excitations at the QCP. We argue that the contact $C_{\rm univ}$ can be measured in state-of-the-art experiments on Bose gases in optical lattices, and in magnetic insulators.